The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1  1  X  1  1  X  1  1  X  2  2  0  2  0 X+2 X+2  1  1  2  1  1  1  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  3  1  1 X+3  1 X+1  3  1  X  1  X  1 X+2 X+2  X X+3  X  1 X+3  3  X X+3
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3 X+3  2  2  0 X+3 X+2  1  3  X X+1  X  3  1  1  1  2  0 X+2  1  1 X+1 X+2
 0  0  0  1  0  3  1  2  3  0 X+1  X  3 X+3  1  X X+3 X+1  3 X+2  X  1  3  2  0  X  1  2  0 X+3  2  X  0 X+2  X
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3 X+1 X+2 X+1 X+2  0  3 X+3 X+1 X+1  1 X+2  3  0  3 X+3  3 X+1 X+1  2 X+3  X

generates a code of length 35 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+286x^28+652x^29+1313x^30+1900x^31+2785x^32+3136x^33+4145x^34+3980x^35+4490x^36+3266x^37+2979x^38+1794x^39+1118x^40+516x^41+267x^42+96x^43+24x^44+14x^45+6x^47

The gray image is a code over GF(2) with n=140, k=15 and d=56.
This code was found by Heurico 1.13 in 7.26 seconds.